In this paper, a novel Follow-the-Perturbed-Leader type algorithm is proposed and analyzed for solving general long-term constrained optimization problems in online manner, where the objective and constraints are not necessarily convex. In each period, random linear perturbation and strongly concave perturbation are incorporated in primal and dual directions, respectively, to the offline oracle, and a global minimax point is searched as solution. Based on two particular definitions of expected static cumulative regret, we derive the first sublinear $O(T^{8/9})$ regret complexity for this class of problems. The proposed algorithm is applied to tackle a long-term (risk) constrained river pollutant source identification problem, demonstrating the validity of the theoretical results and exhibiting superior performance compared to existing method.

Law makers ask President Obama for more water pumping from Sacramento Delta.

Considered by some observers as more of an art than a science, avalanche forecasting involves a unique combination of human observation, analysis, and interpretation. Even the best forecasters only reach about 75% accuracy in their predictions. After all, they are human too and susceptible to bias and imperfection just like the rest of us. One of the biggest challenges in creating an accurate forecast lies in the fact that avalanche danger cannot be precisely measured and is therefore a matter of expert assessment (opinion). That was until last season when the Swiss Institute for Snow and Avalanche Research Group (SLF), a part of the National Swiss Federal Institute for Forest, Snow, and Landscape Research successfully tested a first-of-its-kind, artificial intelligence computer program to assist in its avalanche forecasts.

By the time he stepped onto a bus in downtown Toronto for the first leg of a trip to Lake Tahoe in December 2012, Geoff Hinton hadn't taken a seat for seven years. "I last sat down in 2005," he often said, "and it was a mistake." He first injured his back as a teenager, while lifting a space heater for his mother. As he reached his late fifties, he couldn't sit down without risking a slipped disk, and if it slipped the pain could put him in bed for weeks. So he stopped sitting down.

By the time he stepped onto a bus in downtown Toronto for the first leg of a trip to Lake Tahoe in December 2012, Geoff Hinton hadn't taken a seat for seven years. "I last sat down in 2005," he often said, "and it was a mistake." He first injured his back as a teenager, while lifting a space heater for his mother. As he reached his late fifties, he couldn't sit down without risking a slipped disk, and if it slipped the pain could put him in bed for weeks. So he stopped sitting down.

In this paper, novel gradient based online learning algorithms are developed to investigate an important environmental application: real-time river pollution source identification, which aims at estimating the released mass, the location and the released time of a river pollution source based on downstream sensor data monitoring the pollution concentration. The problem can be formulated as a non-convex loss minimization problem in statistical learning, and our online algorithms have vectorized and adaptive step-sizes to ensure high estimation accuracy on dimensions having different magnitudes. In order to avoid gradient-based method sticking into the saddle points of non-convex loss, the "escaping from saddle points" module and multi-start version of algorithms are derived to further improve the estimation accuracy by searching for the global minimimals of the loss functions. It can be shown theoretically and experimentally $O(N)$ local regret of the algorithms, and the high probability cumulative regret bound $O(N)$ under particular error bound condition on loss functions. A real-life river pollution source identification example shows superior performance of our algorithms than the existing methods in terms of estimating accuracy. The managerial insights for decision maker to use the algorithm in reality are also provided.

A winter storm warning expired in the Lake Tahoe region Friday afternoon. The weather service said 11 inches (28 centimeters) of snow was recorded Thursday night and early Friday at the Northstar ski resort near Truckee, California and about 10 inches (25 centimeters) at Mt. Rose southwest of Reno. Up to 7 inches (18 centimeters) was reported at Heavenly in South Lake Tahoe, California.